FOCUS August/September 2007

FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, May/June, August/September, October, November, and December. Volume 27 Issue 6 Editor: Fernando Gouvêa, Colby College; [email protected] Managing Editor: Carol Baxter, MAA Inside: [email protected] Senior Writer: Harry Waldman, MAA hwald- 4 Mathematical Olympiad Winners Honored at the [email protected] U.S. Department of State Please address advertising inquiries to: 6 U.S. Team Places Fifth in IMO [email protected] 7 Math Circle Summer Teaching Training Institute President: Joseph Gallian 7 Robert Vallin Joins MAA as Associate Director for Student Activities First Vice President: Carl Pomerance, Second Vice President: Deanna Haunsperger, 8 Archives of American Mathematics Spotlight: The Isaac Jacob Secretary: Martha J. Siegel, Associate Schoenberg Papers Secretary: James J. Tattersall, Treasurer: John W. Kenelly 10 FOCUS on Students: Writing a Résumé Executive Director: Tina H. Straley 11 Attend ICME-11 in Monterrey, Mexico Director of Publications for Journals and 12 An Interview with Trachette Jackson Communications: Ivars Peterson 15 The Council on Undergraduate Research as a Resource FOCUS Editorial Board: Donald J. Albers; for Mathematicians Robert Bradley; Joseph Gallian; Jacqueline Giles; Colm Mulcahy; Michael Orrison; Pe- 16 2007 Award Winners for Distinguished Teaching ter Renz; Sharon Cutler Ross; Annie Selden; Hortensia Soto-Johnson; Peter Stanek; Ravi 18 MAA Awards and Prizes at MathFest 2007 Vakil. 20 In Memoriam Letters to the editor should be addressed to 21 Fond Memories of My Friend Deborah Tepper Haimo, 1921-2007 Fernando Gouvêa, Colby College, Dept. of Mathematics, Waterville, ME 04901, or by 22 “Teaching Us to Number Our Days” email to [email protected]. 23 Subsidized Childcare Services at the Joint Mathematics Meetings Subscription and membership questions should be directed to the MAA Customer 23 AWM Announces Search for Executive Director Service Center, 800-331-1622; email: [email protected]; (301) 617-7800 (outside 24 Building a Successful Actuarial Science Program: Five Key Components U.S. and Canada); fax: (301) 206-9789. MAA 26 Café Scientifique Mathematics in the Microbrewery: Headquarters: (202) 387-5200. Fermat Meets Fermentation Copyright © 2007 by the Mathematical Association of America (Incorporated). 28 To and From the Editor Educational institutions may reproduce articles 29 Visiting the “Dark Side” for their own use, but not for sale, provided that the following citation is used: “Reprinted 29 Faculty Fellow Programs to Help High School Students with permission of FOCUS, the newsmagazine of the Mathematical Association of America 30 Teaching Time Savers: Encouraging Contact Early in the Semester (Incorporated).” 31 Employment Opportunities Periodicals postage paid at Washington, DC and additional mailing offices. Postmaster: Send address changes to FOCUS, Mathematical Association of America, P.O. Box 90973, On the cover: 2007 USAMO winners. Photo courtesy of Robert Allen Strawn Washington, DC 20090-0973. ISSN: 0731-2040; Printed in the United States of America.

2 August/September 2007 FOCUS

New Officers Elected

President-Elect: First Vice President: Second Vice President: David M. Bressoud Elizabeth Mayfield Daniel J. Teague Macalester College Hood College North Carolina School of Science and Mathematics The election for MAA officers concluded on May 31, 2007. Conducted using both online voting and paper ballots, the election had a record response rate of 20.99%. A total of 5,078 votes were cast. Of the votes cast, more than 63% were submitted online. The new officers will begin their terms in January at the conclusion of the Joint Mathematics Meetings in 2008.

David Bressoud of Macalester College was chosen as President-Elect, a role he will play during 2008. He will then become the President of the Association for 2009–2010. The two vice presidents will serve a two-year term beginning in 2008.

The MAA is grateful to all candidates for office. They are dedicated members who have devoted their time and effort to the bet- terment of the association. They help to make the MAA what it is.

Bass and Efron Receive National Mathematicians Medal of Science Elected to the National Academy of On July 27, the President of the Unit- Among the 2005 medalists was Sciences ed States awarded the National Medal Bradley Efron, professor of statistics of Science to a stellar group of recipi- and of health research and policy at ents. At a ceremony at the White House, Stanford University. Efron was cited On May 1, 2007, the National Acad- President Bush honored the 2005 and “for his contributions to theoretical emy of Sciences announced the election 2006 recipients of the Medal. More in- and applied statistics, especially the of 72 new members and 18 foreign asso- formation on the event can be found at bootstrap sampling technique; for his ciate members. This year’s class includ- http://www.whitehouse.gov/news/releas- extraordinary geometric insight into ed five mathematicians among the new es/2007/07/20070727-9.html. nonlinear statistical problems; and for members, plus two among the foreign applications in medicine, physics and associates. Elected to membership were Among the 2006 medalists was Hyman astronomy.” Robert L. Bryant of Duke University Bass, professor of mathematics and (recently named Director of MSRI in mathematics education at the Univer- Established in 1959, the National Medal Berkeley), Richard Durrett of Cornell, sity of Michigan. Bass was cited “for of Science and the National Medal of David Gottlieb of Brown, Curtis T. Mc- his fundamental contributions to pure Technology are intended to honor in- Mullen of Harvard, and Harold M. Stark mathematics, especially in the creation dividuals “for pioneering scientific -re of the University of California San Di- of algebraic K-theory, his profound in- search in a range of fields, including ego. Pierre Deligne of the Institute for fluence on mathematics education, and physical, biological, mathematical, so- Advanced Study and John Kingman his service to the mathematics research cial, behavioral and engineering scienc- of the University of Cambridge were and education communities. With his es, that enhances our understanding of elected as foreign associates. Bryant and unique combination of gifts he has had the world and leads to innovations and Stark are members of the MAA. enormous impact over the course of a technologies that give the United States half century.” its global economic edge.” 3 FOCUS August/September 2007 Mathematical Olympiad Winners Honored at the U.S. Department of State

By Lisa Kolbe The 36th USA Mathematical Olym- piad Awards Ceremonies took place in Washington, DC on Sunday and Mon- day, May 20 and 21, 2007. This event honors the twelve winners of the annual USA Mathematical Olympiad exam, the premier high-school level mathemati- cal problem solving competition in the United States. The two-day celebra- tion began with a sponsors’ reception at the MAA headquarters in its newly renovated Carriage House Conference Center. Representatives of the spon- soring organizations of the American Mathematics Competitions, along with members of the MAA Executive Com- mittee, were there to meet and greet the winners and their families. On Monday morning, the winners toured the Crypto- logic Museum at the National Security Winners of the USAMO. Front row from left to right: President Joe Gallian, Sherry Agency and enjoyed a talk from one of Gong, Delong Meng, Alex Zhai, Arnav Tripathy, Tedrick Leung, and Executive Di- the on-site mathematicians on classical rector Tina Straley. Back row from left to right: Adam Hesterberg, Krishanu Sankar, cryptography. Brian Lawrence, Sergei Bernstein, Eric Larson, Haitao Mao, and Jacob Steinhardt.

The 2007 USAMO winners are: The formal awards ceremony, presided twelve. Andrew attends Westford Acad- Sergei Bernstein, Belmont, MA over by MAA President Joseph Gallian, emy in Westford, Massachusetts. took place in the Dean Acheson Audi- Sherry Gong, San Juan, Puerto Rico torium of the State Department where The Robert P. Balles Distinguished Adam Hesterberg, Seattle, WA George Csicsery, writer and indepen- Mathematics Student Award, given to dent film maker, treated the audience each of the twelve winners, is given in Eric Larson, Eugene, OR to a viewing of Hard Problems, a film an effort to recognize and reward their Brian Lawrence, Kensington, MD about the 2006 IMO team. high achievement in the world of math- ematics competitions. Robert P. Balles Tedrick Leung, Winnetka, CA Winners received the USAMO Medal, is a lifelong student of mathematics, Haitao Mao, Vienna, VA named in honor of Gerhard C. Aren- former community college instructor of storff, twice a winner of the USAMO mathematics, and retired businessman Delong Meng, Baton Rouge, LA and a member of the first USA team in who established this generous prize in 2005. Krishanu Sankar, Hastings the International Mathematical Olym- on Hudson, NY piad. The highlight of the evening came when Jacob Steinhardt, Vienna, VA After dinner, Brian Lawrence received the Akamai Foundation Scholarships were presented to the 1st place winner, Arnav Tripathy, Chapel Hill, NC the Samuel L. Greitzer/Murray S. Klam- kin Award for his superior achievement Brian Lawrence, and to Sherry Gong Alex Zhai, Champaign, Il in the Olympiad exam. Dr. James Carl- and Alex Zhai, who tied for 2nd place. son, President of the Clay Mathematics Jonathan Seelig, one of the founders John Marburger III, Director of the Of- Institute, designated Andrew Geng as of Akamai Technologies and the Aka- fice of Science and Technology Policy the ninth CMI Mathematics Olympiad mai Foundation, presented the awards. in the Executive Office of the President, Scholar, noting that Geng best fulfilled These scholarships are in the amounts of was the host at the celebratory reception the prize’s criteria of “elegance, beauty, $20,000 and $15,000 respectively. With and dinner in the Diplomatic Reception imagination, and depth of insight” even these scholarships, the Akamai Founda- Rooms of the U.S. Department of State. though Geng was not among the top tion hopes to encourage these and other

4 August/September 2007 FOCUS students to continue their pursuit of Olympiad (USAMO) exam which was solving Olympiad-style problems. This mathematics education. held on April 24 and 25. The USAMO summer program was funded in part is a six question proof-essay contest, with a grant from the Akamai Founda- The road to the USAMO begins with taking nine hours over two days. The tion. the American Mathematics Contest 10 problems on the USAMO would be (AMC 10) and American Mathematics challenging even to professional math- The final US team for the IMO is se- Contest 12 (AMC 12) exams. In Febru- ematicians. This year’s USAMO prob- lected from among the 12 winners at ary, about 240,000 students from over lems and solutions are available on the the MOSP. Each year since 1974, a 4,000 schools participated in these con- web at the MAA web site: choose the small team of exceptionally talented tests. The AMC 10 and AMC 12 have “Students” tab on the MAA home page high school students has represented the 25 questions from the high school math- and follow the links. United States at the IMO. The IMO is a ematics curriculum to be answered in a rigorous two day competition, again in- timed 75-minute format. The problems The twelve winners and other students cluding problems that would challenge range from easy to quite challenging. who took the Olympiad exam are invited most professional mathematicians. In The top 5% of scorers on the AMC 12 to the Mathematical Olympiad Summer addition to comprehensive mathemati- and the top 1% of scorers on the AMC 10 Program (MOSP) for advanced train- cal knowledge, success on the IMO re- are invited to take the American Invita- ing for the International Mathematical quires truly exceptional mathematical tional Mathematics Exam (AIME). The Olympiad (IMO). The 2007 Mathemati- creativity and inventiveness. The 2007 AIME is a challenging 15-question con- cal Olympiad Summer Program was IMO, held in Hanoi, Vietnam, between test spanning three hours. The difficulty held on the campus of the University of the 19th and 31st of July, was the 48th of the questions ranges from equivalent Nebraska-Lincoln from June 10 to June since Romania initiated the annual com- to the most difficult on the AMC 12 to 30 with 55 students and 15 instructors petition in 1959. United States teams extremely difficult. In March, nearly and graders in attendance. The students have placed within the top countries in 12,000 students took the AIME. received a mix of training on mathemat- all IMOs in which they have participat- ical problem solving, proof-writing and ed. In ten of these, the United States was Based on a combination of scores from deeper instruction on algebra, geometry, awarded first or second place. these two contests, 506 students were number theory, combinatorics, probabil- invited to take the USA Mathematical ity, and trigonometry in preparation for

Filming Hard Problems

By Harry Waldman On the evening of May 21st, attend- Csicsery, perhaps best known among the pressure-filled exams, going on ex- ees at the awards ceremony honoring mathematicians as the director of the cursions, and relaxing after the contest. this year’s U.S.A. Mathematical Olym- documentary N Is a Number: A Portrait Several scenes provided insights into piad (USAMO) winners got a special of Paul Erdös (1993), had the freedom the complicated process of judging and treat. Filmmaker George Paul Csicsery to film the various steps in last year’s scoring the papers. A dramatic closing screened about 45 minutes of clips from Olympiad process. His documentary fol- ceremony unveiled the winners. his planned documentary about U.S. lows select students struggling through participation in the 2006 International the two-day USAMO tests at the Harker Csicsery hopes to have his 90-minute Mathematical Olympiad. School, in Saratoga, CA., and elsewhere documentary — which is produced by last April; the USAMO awards ceremo- the MAA — ready early next year. Hav- Csicsery has titled his film Hard Prob- ny in Washington, D.C., in May; and the ing already shot nearly 90 hours worth lems. He hopes that, in the end, it will subsequent team selection test to decide of film, Csicsery said that he needs only provide an engaging and illuminating the six members of the U.S. IMO team. another 10 or 15 hours of footage before glimpse of teenage mathematicians Csicsery and his crew followed the team he begins the laborious process of editing competing to solve math problems at the to Ljubljana, Slovenia, where 498 young the material into a dramatic story that he highest possible level. It follows up the mathematicians from 90 countries com- hopes will attract audiences unfamiliar book Count Down: Six Kids Vie for Glo- peted in the 2006 IMO. with the trials, tribulations, incredibly ry at the World’s Toughest Math Com- hard work, and triumphs of the young, petition, by Steve Olsen, which docu- The filmmakers photographed the - stu multi-talented U.S. math wizards. mented U.S. participation in the 2001 dents taking part in the colorful opening International Mathematical Olympiad. ceremony, preparing for and enduring

5 FOCUS August/September 2007

U.S. Team Places Fifth in IMO

The U.S. team ended up in fifth place at the 48th International Mathematical Olympiad, held in Hanoi, Vietnam, on July 19–31, 2007. Russia’s team won top honors, scoring 184 out of a possible 252 points. Five of the six members of the Russian team won gold medals.

The U.S. scored 155 points, with two team members (Alex Zhai and Sherry Gong) winning gold medals, three (Bri- an Lawrence, Eric Larson, Arnav Tripa- thy) winning silver, and one (Tedrick Leung) winning bronze.

Following Russia in first place were China (181 points), South Korea (168), and Vietnam (168). The official team Opening ceremonies at the IMO. scores can be seen online at http://www. imo2007.edu.vn/index.php?module=Vi ewResultByCountry.php. Brazil came in 24th, Argentina in 47th. Canada ended up in 27th, just beating the United King- dom, in 26th.

Individual results are also online, at http://www.imo2007.edu.vn/index. php?module=ViewRank. They show that Alex Zhai ended up in 7th place and Sherry Gong in 8th, both with an overall individual score of 32 points. The top individual was Konstantin Matveev of Russia, who scored 35 points. For more information, see the IMO2007 web site at http://www.imo2007.edu.vn/. Students get ready to take the test. “Congratulations to the team for a fine performance on what the leaders agree was a very hard IMO,” said Steve Dun- bar, MAA Director of Competitions. He also thanked team leader Zuming Feng and coach Ian Le. “It’s incredibly hard work,” Dunbar added, “and they did it The United States Team well.” at the 48th IMO

The IMO 2007 closing ceremony took Sherry Gong, Phillips Exeter Academy, Exeter, NH place on July 30, 2007. The 2008 Inter- national Mathematical Olympiad will be Eric Larson, South Eugene High School, Eugene, OR contested in Madrid, Spain. The official Brian Lawrence, Montgomery Blair High School, Silver Spring, MD web site for the IMO is at http://www. imo-official.org/. Tedrick Leung, North Hollywood High School, Winnetka, CA Arnav Tripathy, East Chapel High School, Chapel Hill, NC Photographs provided through the IMO 2007 web site. Alex Zhai. University Laboratory High School, Champaign, IL

6 August/September 2007 FOCUS

Robert Vallin Joins MAA as Associate Math Circle Director for Student Programs Summer Teacher Training Institute Robert W. Vallin of Slippery Rock University has joined MAA headquar- By Bob & Ellen Kaplan ters to become the first-ever Associate Director of Student Programs. The As- sociate Director, working with Michael Since 1994 the Math Circle at Harvard Pearson, Director of Programs and Ser- and Northeastern Universities has made vices, will be involved in all aspects math a source of intense delight for stu- of student membership. This includes dents from 4 to 60 years old. This Janu- working on recruitment and retention ary, our book Out of the Labyrinth: Set- of MAA student members, assisting on ting Mathematics Free was published. events at meetings, and managing grants The book’s description of the Math applications and distributions. Circle has generated a great number of requests, from across the country and Vallin received his bachelor’s degree around the world, for help in creating from the University of Maryland, Col- new branches. We’re ready to set these lege Park, and earned his M.S. and up and are looking for people eager to Ph.D. from North Carolina State Uni- One of his first goals is to turn the MAA run them, who know enough math, un- versity. He has been at SRU since 1992, web site into the “go-to source” for derstand kids, and share our collegial rising to the rank of full professor. The high school, undergraduate, and gradu- rather than competitive approach. For author of several papers on real analy- ate students interested in mathematics details about our approach, see Out of sis and topology, he is also proud of his and mathematical careers. In addition the Labyrinth, and The Art of the Infi- non-research writings, including two ar- to articles on math itself, the future nite, each of whose chapters were Math ticles in Math Horizons. Vallin was very web site will help students find summer Circle classes. See also our web site, at active in the Allegheny Mountain Sec- programs, and obtain job information http://www.themathcircle.org. tion of the MAA, including five years including how to write curriculum vi- as Puzzle Czar and six years as Coor- taes, résumés, and cover letters. As Val- We will therefore hold a training pro- dinator of Student Programs. He is on a lin points out though, this is a position gram from July 6th to 12th, 2008, on two-year leave of absence from Slippery whose responsibilities are in flux. Any the campus of the University of Notre Rock. and all ideas, desires, and suggestions Dame, in South Bend, Indiana. The 20 are welcomed. He can be reached via or so candidates will observe and teach email at [email protected]. small groups of students ranging in age from 4 to 18, discuss math, the teaching of it, and details of running a Math Cir- cle. Each candidate is expected to start a Math Circle after having attended.

The instructors will include Bob and Ellen Kaplan, Amanda Serenevy (Ex- ecutive Director, Riverbend Community Math Center, Mishawaka, Indiana), and Sam Lichtenstein (Harvard University). The Institute is sponsored by the Mathe- matical Sciences Research Institute, the Flom Foundation, the Herbert O. Wolfe Foundation, and the Northern Indiana Science, Mathematics, and Engineer- ing Consortium. Tuition is $750 for the week, room and board included. If you would like to apply, please e-mail us at [email protected].

7 FOCUS August/September 2007 Archives of American Mathematics Spotlight: The Isaac Jacob Schoenberg Papers

By Carol Mead

The Archives of American Mathemat- where he worked on distance geometry ics (AAM) has recently made available and became a Fellow of the Institute for the papers of Isaac “Iso” Schoenberg Advanced Study. After Princeton, he (1903-1990), known for his work in ap- taught at Swarthmore, Colby, and the proximation theory and splines. Sean University of Pennsylvania, where he Heyliger, the AAM’s archival assistant, stayed from 1941 to 1965, with interrup- rehoused the papers and photographs tions for sabbaticals and other projects. into archival-quality folders and boxes and created a more detailed inventory Between 1943 and 1946, Schoenberg of the papers, which will assist our re- joined other mathematicians in the war searchers in accessing the collection. effort in Aberdeen, Maryland; there, he The papers consist of correspondence, was to refine computations of projectile class notes from his student days, re- trajectories on the ENIAC, which he did search and teaching notes, and personal with what he called “Cardinal Spline In- documents. Schoenberg’s wife, Dolly, terpolation and Cardinal Spline Smooth- and a colleague donated the papers to the ence for Schoenberg throughout his life. ing.” He finally settled at the University University of Texas at Austin in 1991. His mother spoke frequently at pub- of Wisconsin in Madison, where he lic meetings and, in the 1920s, acted taught until his retirement in 1973. Correspondence is one highlight of the as a delegate in several Zionist World Schoenberg collection. As the series Congresses in Israel. His father helped After he retired, Schoenberg remained reveals, Schoenberg corresponded with establish agricultural stations in Pales- active in mathematics and pursued other some of the foremost mathematicians tine for young Jewish boys and girls. interests. Among other things, he taught of the twentieth century: Harald Bohr, Throughout his own life, Schoenberg as a guest lecturer at various institutions, Issai Schur, Alexander Ostrowski, Ed- was active in Jewish causes, including wrote many papers, continued to referee mund Landau (his father-in-law), Paul helping family and friends escape from as he had throughout his career for the Erdös, George Pólya, John R. Kline, Europe during the Holocaust. Journal of Approximation Theory, and, and Emil Grosswald. There are also let- in the 1980s, entered the Madison city ters between Schoenberg and his family, The family moved to Jassy, Romania, in sculpture contest with a submission he including his mother, sister and brother- 1910. In 1922, Schoenberg received his created using a mathematical model, in-law, Stefan Wolpe, and the composer, M. A. at the University of Jassy. From the drawings for which are in the col- Joseph Marx. Many of the letters, as 1922 to 1925, he continued his studies lection. well as his notes and other documents, in Germany, where he spent three se- are written in languages other than Eng- mesters at Göttingen and three in Ber- The finding aid for the Schoenberg col- lish: Romanian, German, French, Ital- lin. While in Germany, he studied under lection is at http://www.lib.utexas.edu/ ian, Dutch, and Russian. Landau, Schur, and Ostrowski. In 1926, taro/utcah/00211/cah-00211.html Jassy awarded him a Ph.D. Two years Another highlight is Schoenberg’s ex- later, in 1928, Landau arranged a visit The Archives of American Mathematics tensive research and teaching notes. to the Hebrew University of Jerusalem is located in the Research and Collec- These documents range over his life- (which Landau helped to establish), tions division of the Center for Ameri- time, from his student days to his later from which he returned in 1930. That can History on the University of Texas life, and are, of course, handwritten, re- same year, he married his first wife, at Austin campus. Persons interested in vealing in some notebooks a meticulous Charlotte (Dolli) Landau, Edmund’s conducting research or donating materi- mind. This series, in fact, constitutes the daughter (he remarried in 1950, after als or who have general questions about largest part of the collection and will Charlotte’s death in 1949). the Archives of American Mathematics certainly be of interest to researchers. should contact Carol Mead, Archivist: When Schoenberg was awarded a Rock- [email protected] or (512) Schoenberg was born in Galatz, Roma- efeller fellowship in 1930, he embarked 495-4539. The Archives web page can nia. His father, Jacob Schoenberg, was on a new life in the United States. He be found at http://www.cah.utexas.edu/ an accountant and his mother, Rachel moved around the country, studying first collections/math.php. Segal, a poet. His parents’ devotion to at the University of Chicago, then Har- Zionism provided an important influ- vard, and, from 1933 to1935, Princeton,

8 August/September 2007 FOCUS

Page from Schoenberg’s notebook containing notes from a course taught by Edmund Landau.

9 FOCUS August/September 2007

FOCUS on Students: Writing a Résumé

By Robert W. Vallin A résumé is a listing of your educa- The objective should be one sentence. Nor will making them wide so the typ- tion, skills, activities and achievements. Make sure that it is worded clearly and ing fills more of the page. Choose an It should be a concise history (two pag- is not about what you want. Instead you easy-to-read font rather than a fancy es, maximum) which shows why you are should be showing prospective employ- one. Make sure the paper is profession- qualified for a particular job. Note that a ers what you will do for them. This is al. Putting your résumé on pink paper curriculum vitae (CV) is not the same as where you make your first pitch, show- will certainly stand out: it will be the a résumé. A CV is typically used when ing them that you are who they need prettiest thing in the trash can. applying for an academic or research to hire. The objective “To obtain a position. Just to show one difference, a job where I can teach math to middle Distinctive things (you speak a foreign CV starts at two pages and can go on school students” pales in comparison language, made the Dean’s list, or par- for much longer. (We will discuss how to “Teaching mathematics at a middle ticipated in the Mathematical Contest to write a CV in a future article.) school where creativity and the ability in Modeling) should find an appropri- to motivate students is needed.” ate place if they relate directly to the job A strong résumé is important. A weak or are a special skill or honor. The fact résumé will get your application thrown If you have been interning and working that you are a marathon runner should in the garbage bin and you will never be in the industry, then you have the expe- be included if you are applying to be a considered for the job. rience and should put your jobs out in personal trainer. It is not important if the front and emphasize them. That makes job is research assistant. One exception Writing about yourself can be difficult an experiential résumé. If, on the other to that rule: Many employers are inter- for someone about to graduate from col- hand, you don’t have much relevant ested community service. If you are in- lege. Yes, you did spend the past three work experience, then you should em- volved in charity work, list it. years working at the library, but you fail phasize what you’ve learned to do even to see how this will get you that actuar- if you haven’t had a chance to take your Reading that your email address is ial job. To make matters worse, you just skills out for a spin. That is a functional [email protected] will not got a sample résumé from the Job Place- résumé. So tell your future employer have a positive impact. Open up an ment Center on campus and the woman that you took two classes in Operations email account just for your job search. in this sample was the perfect student, Research and you can solve problems ran most clubs on campus, volunteered in Linear and Dynamic Programming, Don’t bother listing references. They for charity work, and will probably be Queuing Theory, Game Theory and take up space, and you don’t have much. running a multi-billion dollar company Transportation Problems, and that you If an employer wants references, you in two years while you’re working your are well-versed in using different soft- will be asked to provide them. Two more way up to the mailroom. ware packages to find the answer to var- things about references: Make sure you ious modeling applications. This type of ask ahead of time. No one likes a sur- Okay, now take a deep breath and relax. résumé will represent you just fine. prise phone call telling them they have You can just write a functional résumé been listed as a source. Also, make sure rather than an experiential résumé. That Writing about your education is straight- this person will be a good reference. Just is, talk about what you know rather than forward. List your degrees in reverse because you loved Dr. X’s class does not what you’ve done. So forget about her chronological order (most recent first). mean he remembers you or that he has and let’s concentrate on your résumé. You should include the degree, name of a favorable impression of you. Just one the institution, location of the school, statement like, “When he showed up he The basic ingredients for a résumé are major, minor, and dates attended. Only was very attentive,” or worse, “Who?” (not necessarily in order) contact in- if higher than a 3.0 should you bother to and you are sunk. Once your refer- formation, objective, skills and experi- include your grade point average. When ence agrees to help you, a simple note ences, and education. Contact informa- you are coming right out of college, ed- or email reminding him or her of what tion should include your name, regular ucation is usually the first item on your classes you took and how you did will mail and email addresses, and phone résumé after your objective. However, help jog the memory. numbers. Include your personal web as time goes on and you gain more expe- page URL only if the site shows off rience, education tends to work its way Spell-checkers are very nice. Most will your skills related to the job. “Objec- down the page. even correct simple things as you type. tive” specifies what job you are looking However, they will not know that you for. The rest is about why you should get Little details can have a big (often nega- didn’t really mean “tow” but you wanted the job. The goal is to produce a focused tive) impact. Use normal margins. Mak- “two.” In addition, your computer will account alerting employers to who and ing them narrow so your information not indicate that you are being altogeth- what you are. will fit on one page won’t fool anyone. er too complicated and should eschew 10 August/September 2007 FOCUS obfuscation. You should be concise. You Finally, résumés are not a “one size fits This is the first in a series of short do not want long sentences or extra or all” object. Since you are selling a prod- articles for students. The overall complicated words clogging up the pa- uct (yourself), you need to tailor each title for the series will be FOCUS per. The solution: Use other people. At résumé to the prospective buyer (em- on Students. Some of these articles least two people, if not more, should be ployer). Tailoring is easier than ever, will be for undergraduates, others for reading anything you send out, check- since most workplaces have a web site graduate students, and many for all ing for typos, misplaced punctuation, you can browse. If you determine the students. These articles will also be and any of the myriad mistakes we all specific responsibilities of the business posted in the Student section of the make. or department you are applying to, you MAA web site. can make sure your résumé sells you as Do not forget to write down any profes- the person for that job. sional organizations to which you be- Distinctive Documents’ portfolio of long. These show a commitment to your There are lots of resources out there, sample résumés career. If you’re new to all of them, just both online and in print. Help writing http://www.distinctiveweb.com/samples. list the names. If you have been a mem- your résumé can be found at: htm. ber for a long time, show your commit- ment by putting in the years. Groups you Purdue University’s online writing lab Use them so you can put together the may be interested in joining include the résumé workshop package that best fits you and gets you Mathematical Association of America http://owl.english.purdue.edu/work- that job. Good Luck! (MAA), the American Mathematical So- shops/hypertext/ResumeW/. ciety (AMS), the Society for Industrial Robert W. Vallin is the MAA Associate and Applied Mathematics (SIAM), the Monster.com page of samples Director for Student Programs. He wel- Association for Women in Mathemat- http://content.monster.com/samples/ home.aspx. comes questions and comments by email ics (AWM), and the National Council of at [email protected]. Teachers of Mathematics (NCTM).

Attend ICME-11 in Monterrey, Mexico

The Eleventh International Congress on Mathematical Education (ICME-11) will be held in Monterrey, Mexico, on July 6–13, 2008 (see http://www.icme- 11.dk/). Contingent on the funding of a proposal now pending at the National Science Foundation, travel grants will participants to listen to world-renowned tion of Two-Year Colleges, the Ameri- be available and awarded by the close scholars in mathematics and mathemat- can Mathematical Society, and the U. S. of 2007. These grants will be available ics education, and to take part in small, National Commission on Mathematics only to U.S. citizens and will support focused discussion groups on a wide Instruction. travel expenses to ICME-11 that include range of topics. These topics include a hotel accommodations, meal costs, and special emphasis on educating students Elementary, middle, and high school conference registration. They also can from diverse cultures, mathematics edu- teachers and graduate students are be used toward air transportation (on cation for second language learners, the strongly encouraged to apply. Questions American carriers only). Travel grant relationship between research and prac- can be directed to Gail Burrill, burrill@ awardees under this program may not tice in mathematics education, the pro- msu.edu. The travel grant application use funds from other NSF programs to fessional development of mathematics and selection criteria are available on the supplement their international travel teachers; closing the achievement gap, NCTM Web site at http://www.nctm.org/ (airfare to Mexico or subsistence at and information and communication icme.aspx or from Margaret Iding, 116 ICME-11). technology in mathematics education. North Kedzie, Division of Science and Mathematics Education, Michigan State The International Congresses are held A selection committee will review ap- University, East Lansing, MI 48824; every four years and offer a unique op- plications and award the grants for telephone (517) 355-1708, ext. 105; fax portunity for mathematics educators ICME-11 travel. The committee will in- (517) 432-9868, e-mail idingm@msu. from the United States to discuss issues clude representatives from the National edu. The application deadline is Sep- related to mathematics education with Council of Teachers of Mathematics, the tember 30, 2007. Notifications will be international leaders from developed and Mathematical Association of America, made by December 30, 2007. developing countries. Grants will enable the American Mathematical Associa- 11 FOCUS August/September 2007

An Interview with Trachette Jackson

By Joe Gallian Trachette Jackson is associate profes- TJ: I was fortunate enough to partici- TJ: That’s a tough question. In some sor of mathematics at the University pate in an REU with a mathematical bi- ways it’s easier, because we were trained of Michigan. She received a Ph.D. in ologist while at Arizona State. That was the same way, we speak the same lan- Applied Mathematics in 1998 from the my first experience in mathematical bi- guage as far as math and biology go, University of Washington. Her research ology. I got to do a little bit of differen- and our ideas often complement each focuses on modeling the growth and tial equations and see how they played other’s. It’s kind of nice to talk to some- control of cancer. a role in predicting growth of bacterial one who complements you that way. colonies. It was really great. Jackson has held post-doctoral posi- Learning to talk math biology to biolo- tions at Duke University, the Institute JG: Now mathematical biology is about gists has been a process. It started when of Mathematics and its Applications at the hottest field in mathematics. When I was in graduate school. Luckily, my the University of Minnesota, and the you got started was it considered a hot advisor pushed us out into the sciences. National Health and Environmental Ef- field? I was interested in cancer, so he made fects Research Laboratory of the Envi- me talk to people who were working on ronmental Protection Agency. She is the TJ: I think that it was just coming to cancer. I think that the fact that I started recipient of an Alfred P. Sloan Research the fore. I hadn’t heard of mathematical learning to communicate at that stage in Fellowship and the Career Enhancement biology and I had no idea that the two my career has helped me today. That’s Fellowship from the Woodrow Wilson subjects could connect. I think that the something that I try to do with my stu- National Foundation. At the University faculty member whom I worked with dents: to make sure that they’re learning of Michigan she received the Amoco was one of the only people doing it at to communicate, to understand prob- Faculty Undergraduate Teaching Award. Arizona State. I think that I was lucky lems and be able to communicate what She is currently a co-PI on an NSF grant to catch the wave at the starting point. I they’ve done mathematically to the au- for a revolutionary program that will al- could have easily gone down a different dience that it’s intended for, which is low undergraduate students to develop path, so that was very lucky. biologists. knowledge and acquire skills in research areas that are at the interface of biology JG: So was that undergraduate research JG: Your research must require you to and mathematics. Jackson is a frequent program pivotal? spend a lot of time learning biology. invited lecturer at conferences and uni- versities. TJ: Yes, it was. Research experience, as TJ: Yes. My experience with biology well as a particular talk that I happened in high school and as an undergraduate Joe Gallian: Did you start out as a math to go to as an undergraduate, were huge was very minimal, so when I hit gradu- major in undergraduate school at Ari- factors in my decision to go into math- ate school and made a commitment to zona State? ematical biology. Going to talks was working on biological problems, I had required as part of the REU program; I to really hit the books. I focused mainly Trachette Jackson: No, I didn’t. I en- would probably never have drifted into on the biology that was relevant to can- tered Arizona State as an engineering a math seminar as an undergraduate if it cer. By no means am I an expert on biol- major. I planned to go into aerospace en- weren’t required. I heard a talk by James ogy, I don’t even have anywhere near a gineering with hopes of maybe becom- Murray on how a leopard gets his spots. degree in biology, but my strategy has ing an astronaut or something grand like I didn’t understand why this talk should been to focus on the particular aspects that. But I had the good fortune to attend be in the math department because it that I work on. several math classes at Arizona State didn’t seem like it should have anything as a high school student, and I caught to do with math. Even though I didn’t What I find really exciting for those the interest of several math professors. understand very much of the talk, I saw who are coming up now is that they They asked me what I was going to ma- that there were some exciting possibili- don’t have to do that, they don’t have jor in, and I told them engineering. They ties in mathematical biology, and I knew to be trained as a mathematician and asked why, and I said because I’m good that that was the direction that I wanted then learn biology or be trained as a bi- at math. I thought that that was the natu- to go in when I went on to graduate ologist and learn some math later. There ral answer. They said “Why don’t you school. are many programs now that are trying major in math?” So I ended up changing to get dual training at the very earliest my major in that first semester. JG: You and your husband sometimes stages in place. I find that prospect re- work together on research projects. Is ally exciting for these students and I try JG: Did you participate in research as that harder or easier than working with to convey that enthusiasm so they see an undergraduate? someone who is just a colleague? what an opportunity they have, an op-

12 August/September 2007 FOCUS portunity that I wish I had when I was ology and Mathematics Education and look at Michigan, it might not be easy to coming up. Research Group Experiences. The goal see from the outside how much mathe- is to bring teams of undergraduates to- matical biology is being done there. This JG: Do you attend biology colloquia gether to work for an extended period of group is trying to bring all those people and seminars? time on projects at the interface of math together, at least for short periods of and biology. The way we plan to do it time. There’s a seminar series, a distin- TJ: Yes, I do, even when the thrust isn’t is to have two students who are concen- guished lecture series, graduate students mathematical. I think that those are trating in math working with two stu- do a brown bag lunch where they talk sometimes the most exciting. I always do dents who are concentrating in biology about their own research to their peers. that when I am looking for a new proj- to form a four-person team co-mentored I currently have four graduate students ect. That’s the best place to find a new by a faculty member from the math- and two post-docs and one undergradu- project, at a biological seminar. You see ematical sciences and a faculty member ate working with me. all kinds of experiments, and the wheels from the biological sciences. They’ll start turning about what kind of quanti- begin this summer with some intensive JG: Do you a have special interest in tative things you can do to help address training to get everyone up to speed and getting students from underrepresented the questions they’re interested in, and on the same page and then they’ll work groups involved in undergraduate re- often that leads to collaborations. on research projects during the year and search? take a specialized set of courses. JG: I know someone who got interested TJ: Yes, I do. I have an interest in that in mathematical biology and started at- The goal really is to get them to do at the undergraduate and at the gradu- tending weekly biology seminars. He something that is cutting edge. The re- ate level. At Michigan, it’s hard to find was surprised by the amount of arguing search projects, which I think is really underrepresented minorities who are and criticism that went on. Have you the most exciting part of this, are com- majoring in math. So what I do is spend been to biology seminars like that? ing from labs right there on campus, and time as an undergraduate advisor, so in some cases are extending existing that I get to see a wide variety of stu- TJ: I have been to a few of those. At collaborations, but what I think is really dents, some of whom may be thinking journal clubs where a paper is assigned, exciting is that new collaborations will about math, and I get to give my input people rip it apart. It’s a different culture be forming between the students and the and maybe mentor and nurture the un- over there. The students in biology seem two faculty members. derrepresented minorities who I see in to learn early that it’s okay to critique that way. published works. In math and even in JG: That’s another significant differ- applied math, when you read a paper, ence between math and biology. Biolo- Teaching introductory courses has also you believe everything that’s in it. The gists seem to tend to work in fairly large helped me to find students who might biologists are on the other end of the teams. want to major in math. Many students spectrum. They go really, really deeply from underrepresented groups come into what’s been done before. I think TJ: Yes, they work in large labs and in without testing out of calculus, so that that’s good, because they can then in large groups, and that is very differ- they’re taking calculus or maybe a see how to advance science by doing ent from the way mathematicians tend course before calculus. That’s where things differently. to work. I think that it’s good for stu- I find a lot of students who just need a dents who are concentrating in math to little encouragement to do well in math, JG: In math we have proofs, and once see how biologists run labs and it’s also and then they can go on and declare a something has been proven it’s very dif- good for the biologists to see how math- math major and actually succeed in it. ficult to overturn it. So maybe there is ematicians normally work. They need to So it’s not easy to find them, but once more room for speculation in biology. find a happy medium if their goal is to you find them it only takes a little en- be a scientist who works on problems couragement and for someone to show TJ: Yes, there definitely is. And in math, that lie right at the middle of the two. a little interest for them to realize this if you read a proof that’s really elegant could actually be a possibility for them. and beautiful, that’s the end point, and JG: Tell me about the mathematical bi- people don’t ask themselves “Could I ology research group at Michigan. JG: A major problem that math has is have done this differently?” that when students come out of high TJ: There are only about four serious school, they don’t think of math as a ca- JG: Your NSF SUBMERGE grant math biologists in the department, plus reer, even if they’re good at math. seems like a very exciting project. a few others who dabble in math biol- ogy around the periphery of the subject. TJ: Our web site has a link that address- TJ: It’s brand new, and we’re going The four of us make up the core, but the es that question. It shows some career to start it this summer. SUBMERGE group also includes faculty from biology choices for mathematicians. It shows stands for Supplying Undergraduate Bi- and from the medical school. When you where some of our undergraduates have

13 FOCUS August/September 2007 gone, and what career paths some of our courses in math biology, and they sort of JG: Have you used any combinatorics? graduates have taken so that undergrad- took off. It’s been a great experience. uates can see some of their options and TJ: No, I haven’t, but I have sat on a dis- that there is a wide variety of opportuni- JG: Does Michigan have a separate cal- sertation committee for several students ties. culus course for biology students? who were interested in bioinformatics and used combinatorial techniques. But JG: Have you written joint papers with TJ: No, we don’t yet. But as part of I haven’t used it in my own research. biologists? Where might these be pub- the SUBMERGE, that’s something that I do think that that is a way to bridge lished? could definitely happen. We’re talking more pure approaches and the biologi- about getting calculus modules put into cal sciences. People sometimes ask me TJ: Yes, I often write joint papers with intro biology courses and putting biol- if I always have to use differential equa- biologists. In fact, the first papers that I ogy modules into a calculus course. At tions. The answer is no, biology is so did when I was a graduate student were the later levels, such as in differential immense that there are questions that with biologists, and I have continued to equations, we’re trying to do something can be answered with almost any type work with biologists. My most exciting similar. We’re trying to get some experi- of mathematics. work is hopefully still to come, and I will mental components put into the model- definitely have biological co-authors. ing courses, where part of the course JG: What goals do you have for your- will be to do some simple experiments self 5 to 10 years down the line? There are math biology journals that to collect data and then model and ana- focus on publishing mathematical bi- lyze it. TJ: Hopefully I will be a full profes- ology papers, and I publish in those. I sor! I hope to still be doing research at really strive to publish in the biological JG: You said that there might be cal- the level that I’m doing it now, but at journals of my fields. My field is cancer culus modules put in biology courses. the same time I want to start switch- research, and the very top journals in Does that mean that biology students ing gears to really focus on the issue this field are Cancer Research and The take calculus before biology? of minority graduate education. I really British Journal of Cancer. When I was would like to see the university that I’m starting out, it was very uncommon to TJ: No, not right now, and that’s a associated with have significant num- see a mathematical modeling paper in problem. One of the biggest problems bers. Right now we’re not there, but I one of those journals. Now it is becom- we have is that students who are major- think that there are a handful of us who ing a little more commonplace. But it’s ing in biology often wait until the very are committed to working on that. Being still very difficult to get a mathematical end to take their math requirements. We still relatively junior, there has to be a modeling paper in the top biological want to get that turned around a little bit, trade-off between research and the other journals. and maybe pilot something where math activities that you want to do. I see my- is incorporated gently into one of the bi- self in a few years being able to handle JG: Some major research universities ology courses. switching gears a little bit better. are making mathematical biology an area of special focus by putting a lot of JG: It seems that everything you do JG: Is there anything else you would resources into it. Is that true at Michi- uses differential equations. Do you use like to point out? gan? any discrete mathematics? TJ: It really does seem that luck has TJ: Yes, Michigan is very interested in TJ: It’s true that most of my work uses followed me throughout my career. I promoting math biology, and they are continuous methods. But now there’s a went to the University of Washington in putting their money where their mouth big buzz in the field for combining the hopes of working with a person I saw is, so to speak. We had a college-wide two, looking at both continuous and dis- give a talk, and it worked out, I ended up theme semester in mathematical biol- crete methods. For some things it makes getting my dissertation under Jim Mur- ogy that got a lot of recognition for our sense to use continuous models, but ray. I also had the good fortune of being group and for the subject. for other things, like individual cells, mentored as a post-doc by another lead- it makes sense to treat them as discrete ing figure in math biology, Mike Reed at JG: I noticed that you received a faculty entities. I have a student right now who Duke. I think I really have had these an- award for teaching. Was there some par- is building a model of blood vessel for- gels on my shoulder throughout my ca- ticular facet of teaching that was a major mation, and we are using discrete com- reer, and I hope to be the angel on some- factor in your getting it? ponents for cells and continuous com- one’s shoulder as they come along. ponents for chemicals and things that TJ: When I first got to Michigan, the govern how they move. This is really only math biologist they had left, so my first venture into discrete modeling, I could come in and start developing and I’m finding it very interesting and courses. I started with the undergraduate very applicable to the work I do.

14 August/September 2007 FOCUS The Council on Undergraduate Research as a Resource for Mathematicians

By Thomas Q. Sibley

The MAA CUPM Subcommittee on have student mem- undergraduate Research by Undergraduates would like bers. “Posters on the research. CUR to inform the mathematics community Hill,” a different sort supports the in- about the many organizations involved of lobbying effort stitutionalization in the promotion of undergraduate re- by CUR, showcases of undergraduate search. In particular, attention should be undergraduates talk- research through- called to the Council on Undergraduate ing about their re- out colleges and Research (CUR), an interdisciplinary search to senators universities. For organization committed to fostering un- and representatives. instance, a CUR dergraduate research. Recently, this suc- institute “Insti- cessful program has been imitated at a tutionalizing Undergraduate Research” Started in 1978 by a group of chemists, number of state capitols. Since 2001 the helps teams of faculty and administra- CUR focuses on enabling undergradu- Mathematics/Computer Science Divi- tors make undergraduate research a ate institutions to compete for research sion of CUR has sponsored prizes for permanent focus throughout a school grants from the NSF and other govern- the best undergraduate research talks (http://www.cur.org/institutes). mental funding sources. Over time CUR at the MAA and Pi Mu Epsilon paper has broadened its focus and developed sessions at MathFest. Although other Schools that are institutional members an increasingly multidisciplinary flavor. organizations give prizes there, only the get several individual memberships, During the 80s it added divisions for CUR prizes are specifically for original which tend to go to administrators. other natural sciences and opened its research. These memberships can help educate membership to faculty and administra- administrators on the importance and tors from all institutions. Our own MAA Another event featuring undergraduate challenges of undergraduate research, President, Joe Gallian, was a founding research, NCUR, is often confused with as well as the range of what research is. member of the Mathematics/Computer CUR. NCUR, the National Conferences Since too few non-mathematicians un- Science division in 1989. Since then, on Undergraduate Research, sponsors derstand the nature of mathematical re- CUR has added divisions in the social an annual conference of the same name search, mathematicians can benefit from sciences, an at-large division (primarily where undergraduates can present their any such increased understanding and for administrators) and one for directors research. Although CUR and NCUR as appreciation. We would also suggest the of undergraduate research programs. organizations talk to each other, they are article by the CUPM Subcommittee on distinct. the costs and benefits of mathematics Funding for undergraduate research has research by undergraduates to faculty been a major focus for CUR. Joe Gallian How can mathematicians benefit from and the institution. See http://www.maa. notes that CUR was instrumental in lob- CUR? Every two years CUR hosts a org/cupm/CUPM-UG-research.pdf. bying for the Research Experiences for national conference on fostering un- Undergraduates program (REU) after dergraduate research, filled with work- CUR welcomes everyone who wants to the Reagan administration phased out shops, talks and opportunities to interact learn more about mentoring and sup- its predecessor (URP) in the 80s. CUR with others committed to undergraduate porting undergraduate research as well didn’t just wait for government-funded research. (The next one will be June as all with ideas to share. Visit the CUR REUs to bolster summer research op- 21–24, 2008 at the College of St. Bene- website at http://www.CUR.org. portunities. It also found corporate dict in Minnesota.) Secondly, mathema- funding to support undergraduates do- ticians can use electronic and in-person Thomas Q. Sibley is professor of math- ing summer research at colleges and connections through CUR to develop in- ematics at St. John’s University and the universities. In recent years these funds terdisciplinary collaborations for under- College of St. Benedict. He is currently have dried up, but they provided impor- graduate research. Also, CUR provides the president of the North Central Sec- tant interim support. Many schools now information and advice on supporting tion of the MAA. provide their own funding for under- and mentoring undergraduate research graduate research, in addition to gov- in its journal, pamphlets, institutes, web ernmental and other funding. pages, and personal exchanges.

CUR has some direct impact on under- Some broader initiatives by CUR ben- graduates, even though CUR does not efit all faculty members mentoring

15 FOCUS August/September 2007 2007 Award Winners for

Pacific Northwest

North Central

Duane DeTemple Washington State University

Northern California, Intermountain Nevada, Hawaii Karen Saxe Macalester College

Oklahoma-Arkansas

William Fisher Peter Alfeld California State University, University of Utah Chico

Southern California- Nevada

Joan E. Bell Northeastern University

Jon McCammond University of California, Santa Barbara Texas

Winners Not Pictured:

Illinois Section: Dennis Schneider, Knox College

Nebraska-SE South Dakota Section: Jim Johnson, Doane College Minerva Cordero-Epperson Rocky Mountain Section: The University of Texas Lynne Ipiña, University of Wyoming at Arlington

Southwestern Section: Glenn Hurlbert, Arizona State University

16 August/September 2007 FOCUS Distinguished Teaching

Northeastern

Michigan Seaway

Kenneth I. Gross University of Vermont

Ohio Eddie Cheng Oakland University Alan D. Taylor Union College Metro New York

EPaDel Kentucky

Bill Higgins Wittenberg University Walter Meyer Adelphi University Missouri Annalisa Crannell Chris Christensen Franklin and Marshall College Northern Kentucky University Md-Dc-Va

Southeastern

Dr. Ken Lee Missouri Western State University

Louisiana-Mississippi Mike Bardzell Salisbury University

David Sumner University of South Carolina

Florida

Randall G. Wills Southeastern Louisiana University

Jacci White Saint Leo University 17 FOCUS August/September 2007

MAA Prizes and Awards at MathFest 2007

Every year, the MAA announces several prizes and awards at MathFest, including the Alder Awards for distinguished teaching by a beginning college or university mathematics faculty member and the various awards for expository writing published in one of the Association’s publications. This year’s winners are listed below. More information can be found on the MAA web site, including citations, responses, and photographs of the winners. More photographs will appear in the October issue of FOCUS.

Carl B. Allendoerfer Awards Harold P. Boas For expository articles published in Mathematics Magazine “Reflections on the Arbelos” American Mathematical Monthly Carol V. Lutzer vol. 113, no. 3, 2006, pp. 236–249. “Hammer Juggling, Rotational Instability and Eigenvalues” Michael Mossinghoff Mathematics Magazine “A $1 Problem” Vol. 79, no. 4, 2006, pp. 243–250. American Mathematical Monthly vol. 113, no. 5, 2006, pp. 385–402. Saul Stahl “The Evolution of the Normal Distribution” George Pólya Awards Mathematics Magazine For expository articles published in the College Vol. 79, no. 2, 2006, pp. 96–113. Mathematics Journal

Trevor Evans Awards Richard Jerrard, Joel Schneider, Ralph Smallberg, For expository articles published in Math Horizons and John Wetzel “Straw in a Box” Robert Bosch College Mathematics Journal “Opt Art” vol. 37, no. 2, March 2006, pp. 93–102. Math Horizons February 2006, pp 6–9. Allen Schwenk “Distortion of Average Class Size: Adrian Rice and Eve Torrence The Lake Wobegon Effect” “Lewis Carroll’s Condensation Method for College Mathematics Journal Evaluating Determinants” vol. 37, no. 4, September 2006, pp. 293–296. Math Horizons November 2006, pp. 12–15. Merten M. Hasse Prize For a noteworthy expository paper appearing in an MAA pub- Lester R. Ford Awards lication one of whose authors is a younger mathematician For expository articles published in The American Mathematical Monthly Franklin Mendivil “Fractals, Graphs, and Fields” Andrew Granville and Greg Martin American Mathematical Monthly “Prime Number Races” Vol. 110, No. 6, June 2003, pp. 503–515. American Mathematical Monthly Vol. 113, no. 1, 2006, pp. 1–33. Henry L. Alder Award For Distinguished Teaching by a Beginning College or Uni- Jeffrey C. Lagarias versity Mathematics Faculty Member “Wild and Wooley Numbers” American Mathematical Monthly Timothy Chartier Vol. 113, no. 2, 2006, pp. 97–108. Davidson College

Lluís Bibiloni, Jaume Paradís and Pelegrí Viader Satyan Devadoss “On a Series of Goldbach and Euler” Williams College American Mathematical Monthly Vol. 113, no. 3, 2006, pp. 206–220. Darren Narayan Rochester Institute of Technology

18 August/September 2007 FOCUS Introducing… a new column on MAA Online

Experiences Program Models Research Projects

Funding Sources Conferences Research Articles

This new column will provide an array of resources for faculty interested in mentoring and promoting undergraduate research in mathematics. We invite your submissions with student and faculty experiences, research articles, announcements and other ideas to encourage student and faculty participation in undergraduate research.

Send submissions to co-editors: Darren A. Narayan, [email protected] Sarah Spence Adams, [email protected]

19 FOCUS August/September 2007 In Memoriam

Deborah Tepper Haimo, 1921–2007 Portsmouth to help develop methods for all I look forward to quite a few years of “degaussing” — that is, demagnetizing pleasure and pride as I watch the MAA Former MAA President Deborah Tepper — transport ships that might be targets prosper and grow in service to collegiate Haimo died at the age of 85 in Clare- of German U-boats. Near the close of mathematics.” mont, Calif. on May 17, 2007. Haimo the war, Todd prevented Allied forces served as MAA President in 1991–92. from turning to rubble the Mathemati- His change of focus included moving to During her tenure as president, she cal Research Institute, in Oberwolfach, Annapolis, Md., to take up sailing with helped reorganize the MAA’s committee where the University of Freiburg was his wife, Shirley. “A.B.” is survived by structure, created the Franklin and Deb- sheltering its mathematicians. It was his wife of more than 50 years, Shirley; orah Tepper Haimo award honoring out- “probably the best thing I ever did for his children David, Mark, Peter, and standing teaching, and encouraged the mathematics,” he later said. Daniel; and several grandchildren. He’ll participation of women in mathematics be missed by all of us, both inside and at every level and in the MAA. After the war, Todd returned to teach- outside the Association, who knew and ing at King’s College, developing a spe- loved him. Haimo attended Radcliffe College as an cialty in numerical analysis. In 1947, he undergraduate and received her Ph.D. and his wife moved to UCLA to help es- A longer article on Willcox will appear from Harvard in 1964. She went on to tablish the National Applied Mathemat- in a future issue of FOCUS. a distinguished teaching career at the ics Laboratories, part of the National University of Missouri-St. Louis. After Bureau of Standards. Todd later became James Eells, 1926 – 2007 retirement she moved to La Jolla, CA, chief of the Bureau’s computation labo- and became active in the department of ratory, in Washington, DC, helping to In our May-June issue, we included mathematics at the University of Cali- launch the field of high-speed computer (page 17) a short notice on the death of fornia, San Diego, participating in semi- programming and analysis. In 1957, James Eells. Unfortunately, we spelled nars and social events. Todd moved to Caltech, where he and Eells’ name incorrectly. We deeply re- his wife remained until retirement. gret the error. To make amends, we print MAA Secretary Martha Siegel said, here a corrected notice. “Many of us who knew and worked For an in-depth profile of John Todd, see with Debbie found her an excellent role “John Todd — Numerical Mathematics James Eells died on February 14 at the model, a person with high personal and Pioneer,” published in the January 2007 age of 80. Eells graduated from Bow- professional standards. She had a strong issue of College Mathematics Journal. doin College and then from Harvard work ethic in everything she tackled. She made many significant contributions to A. B. Willcox, 1925–2007 University. His doctoral work was com- the MAA when she served as President pleted in 1954, under Hassler Whitney. in 1991 and 1992. Our Association owes Former MAA Executive Director Al- After holding several prestigious posi- a great deal to her leadership.” fred B. Willcox died on May 15, 2007, tions in the U.S., he moved to the Unit- at age 81. Affectionately known as ed Kingdom and became Professor of Deborah Tepper Haimo is survived by “A.B.,” Willcox taught at Amherst Col- Analysis at the University of Warwick. five children; Zara, Ethan, Nina, Leah, lege, served as Executive Director of He was later named the first head of the and Varda Tepper Haimo, 13 grandchil- the Committee on the Undergraduate mathematics group at the International dren and one great grandchild. Program in Mathematics, and in 1968 Center of Theoretical Physics in Trieste, became MAA’s second Executive Di- Italy. His research dealt with harmonic See page 21 for an extended article on rector. maps, geometric evolutions, and sto- Haimo. chastic analysis. Announcing his retirement in FOCUS John Todd, 1911–2007 in June 1989, when the MAA’s member- In Memoriam Online ship stood at “27,500 members in good http://www.maa.org/news/inmemo- John “Jack” Todd, a pioneer in com- standing,” Willcox said, “our operation- riam.html. puting and numerical analysis, died in al base is strong, our programs thrive, Pasadena, CA on June 21. Born in 1911, and our confidence in the future strength Todd grew up in Northern Ireland and of the Association is supreme.” We maintain an In Memoriam page at did his graduate studies at Cambridge the MAA web site. It contains short University under J.E. Littlewood and “I have enjoyed and been rewarded and death notices for MAA members and G.H. Hardy. In 1938, he married the stimulated by twenty-one years as your other people known to our members. mathematician Olga Taussky, who be- Executive Director. As everyone over Short obituaries for this page may be came one of the first women to make a 60 knows, one pays a toll for so many submitted directly to Carol Baxter at mark in 20th-century mathematics. Dur- years of sustained stimulation. I look [email protected]. ing World War II, Todd was assigned to forward to a change of focus… Most of 20 August/September 2007 FOCUS Fond Memories of My Friend Deborah Tepper Haimo, 1921-2007

By Carole B. Lacampagne But Debbie’s service to academia ex- The year was 1988, the place Vienna, tended beyond the MAA. She served Austria. She was striding one step ahead on numerous national and international of me, dragging her wheely suitcase, panels and committees on mathematics head held high, determined, a woman and its teaching, was a trustee of Rad- on a mission. This is how I’ll always re- cliffe College, and was a member of the member my friend Debbie Haimo. Board of Overseers of Harvard Univer- sity. Debbie had a rather exotic childhood — she was born in Odessa, Ukraine, At the time of her retirement, she told and lived in Israel before coming to the me that she was tired of the cold weather United States when she was 11. Her fa- and planned to move to La Jolla, Cali- ther was a portrait painter, which precip- fornia, where it was always warm, and itated the family wandering around the she could have a wonderful view of world. Wherever Debbie lived, many of the Pacific Ocean. Despite my warning her father’s portraits adorned the walls against moving to an entirely new com- of her homes. Debbie’s involvement with the MAA munity with few friends and relatives dates back to her graduate days. Over nearby, Debbie did indeed make that Debbie spent her undergraduate years the years, she served on numerous MAA move. She bought a lovely condomini- at Radcliffe College, with considerable committees — on the Teaching of Un- um overlooking the ocean where she en- time in mathematics courses at Harvard. dergraduate Mathematics, the Nominat- tertained many of us at the Joint Meet- It was in a Harvard graduate course in ing Committee, the Program Committee, ings in San Diego. Her mathematical mathematics that she met her husband and the Committee for the Participation interests turned to solving California’s Franklin. When Franklin received his of Women in Mathematics. These activ- problems with school mathematics and Ph.D., they were married. Her own ities culminated in her serving as Presi- to attending the many interesting math- Ph.D. was delayed by bearing and rais- dent of the MAA (1991-1992). Her goal ematics seminars—and the parties that ing five children and an interruption as President was to restructure the very followed at—the University of Califor- caused by her then thesis advisor Has- cumbersome committees into councils. nia, San Diego, where she held an hon- sler Whitney’s move to the Institute for According to Marcia Sward, orary position. Advanced Study. She finally completed it under David Widder in 1964. Most of One goal which Debbie did not Debbie was one of a generation of Debbie’s work was in harmonic analy- achieve was reduction in the number women in mathematics who set aside sis relating to special equations, the heat of committees. Knowing how deter- or downgraded their careers in math- equation and extensions of it, and vari- mined she could be, the staff and of- ematics temporarily while helping their ous integral transformations and series, ficers tended to believe her when she husbands begin their careers and raising often associated with Bessel functions said she was going to end her term a brood of talented children. Today’s or Hermite and Laguerre polynomials. as President with fewer committees young women in mathematics face dif- She published over 40 mathematics pa- that when she started. Rumor has it ferent problems, but I hope they will pers, two of them with Richard Askey, that there were some under-the-table look back fondly at the problems and who remained her friend and colleague bets on this! But at the end of her triumphs that Deborah Tepper Haimo throughout her life. time, there were several more com- and other women in mathematics in the mittees than in the beginning. There mid-twentieth century faced. With Franklin at Washington University were just too many good things to be in St. Louis, and five children to raise, done and too many people willing to Many of us who cared so deeply about Debbie found time to teach mathemat- devote endless hours to making them her, last saw Debbie at the 2004 Joint ics courses at Washington University happen. Debbie was just too good a Meetings in Phoenix — still striding and Southern Illinois University and to role model! along, with the help of her detested cane, serve as editor of the “Math Notes” of still determined, a woman on a mission. the American Mathematical Monthly A lasting contribution to her concern We will all miss her. with Franklin. In 1968 she was hired for mathematics teaching at the college After working at Northern Illinois Uni- by the University of Missouri-St. Louis level was her instituting an annual MAA versity, DoE, RAND, and the MSEB, to build their mathematics department, award, the Deborah and Franklin Tepper Carole Lacampagne is now semi-re- which she did. She remained there until Haimo Awards for Distinguished Col- tired. She thanks Richard Askey, Jerry her retirement in 1992. lege and University Teaching of Math- Porter, and Marcia Sward for sharing ematics. their memories of Debbie. 21 FOCUS August/September 2007 “Teaching Us to Number Our Days”

By Jacqueline Brannon Giles

Years ago, the University of Hous- Later, Jerry Porter led the Professional flowed into my professional life, I won- ton–Downtown hosted an MAA meeting Development Committee, and he men- der about what flowed out of my profes- in Houston, Texas, at the Sofitel Hotel, tored me, and strategically positioned sional life during my many days of in- near the George Bush Intercontinental me with Bonnie Gold. Well, the rest is volvement, from the level of the Board Airport. I was encouraged to attend that history. of Governors to various committees. meeting. Al Willcox helped me enter the door, and Debbie Haimo ushered me Another memory is my phone call in Let us be wise and continue to strive for into a more functional position. August 1989 to Dr. Willcox. Willcox a strong, diverse organization, for we nominated me to the early version of the can only honor what they did by build- In 1990, my article on “Black Pioneers Joint Policy Board for Mathematics. So ing on the foundation laid by them. I am in Mathematics” was published, and 2007 is the year that we have lost two certain that there are others like me who while I was being introduced at the MAA great mentors: Haimo, the former MAA say “thank you” to the families who meeting, Florence Fasanelli told Haimo President, and Willcox, the 21 year vet- shared these wonderful people with us. about my article. She was very gracious eran Executive Director of MAA. and kind, and she asked me whether I Jackie Giles is a member of the FOCUS might want to get more involved with The departures of Willcox and Haimo editorial board. She teaches at Central MAA. I said “yes.” A few weeks passed from this realm of my (our) reality re- College, part of the Houston Commu- and then I was nominated to be a part mind me to be grateful to all who have nity College System. of the Professional Development Com- contributed to those of us who aspired mittee, led by Beverly Anderson of the to make contributions in this great orga- University of the District of Columbia. nization. As I recall how what they did

Found Math Our resident mathematician, Cheapano Fibonacci, has come up with some amazingly low fares for you — as low as $1 each way! Cheapano comes from a long line of famous Fibo- nacci mathematicians, but he is the first to offer fares for only $1* each way! We invite you to follow Cheapano’s number sequence to great fare sales. We are offering fares from $1*, $2*, $3*, $5*, $8*, $13*, $21*, $34*, $55*, $89*, $144* and $233* each way. Even though the Fibonacci numbers keep going up and up, Cheapano stopped at 233; we are an Ultra Low Cost Carrier after all!

(Spirit Air web site, June 27, 2007; thanks to Jenny Quinn)

22 August/September 2007 FOCUS Subsidized Childcare Services at the Joint Mathematics Meetings

“Love it! And the boys do too!” The American Mathematical Society the older children, specially designed so parents can be responsible for meals for and the Mathematical Association of that children can make friends easily in their children. America are pleased to announce that a comfortable, safe, and happy environ- for the fourth year they are offering and ment. Registration will be open in September significantly subsidizing childcare - ser 2007, with the deadline of December vices at the Joint Mathematics Meetings The feedback on the service in past 9, 2007. Availability is limited and will (JMM) — this time in San Diego, CA, meetings has been enthusiastic: “Very be handled on a first-come, first-served January 6–9, 2008. Child care will be convenient and useful. I hope it will basis. The registration fee is $30 per offered to parents through KiddieCorp, continue to be offered.” “I really appre- family (nonrefundable), plus $9 per an organization that has been providing ciated the service.” “Wonderful! Please hour per child, $7 per hour per child for high quality programs for children of do it again!” graduate students. Full payment is due all ages at meetings throughout the U.S. at the time of registration with Kiddi- and Canada since 1986. The dates and times for the program are eCorp. To learn more about the service, Sunday through Wednesday, January policies regarding cancellation and late Parents registered as participants at JMM 6–9, 2008, 8:00 a.m. to 5:00 p.m. each child pick-up fees, and to register, go can take their children for a fun few day. It will be located at the San Diego to https://www.kiddiecorp.com/jmmkids. days and still enjoy the meeting. While Marriott. The service is for children 6 htm or call KiddieCorp at (858) 455- attendees are in sessions KiddieCorp months through 12 years old. Parents are 1718 to request a form. will engage children in popular tried encouraged to bring snacks and bever- and true games and activities including ages for their children but items such as Come to the Joint Mathematics Meet- arts & crafts, music & movement, board juice boxes, Cheerios and crackers will ings in San Diego, January 6-9: Meet games, story time, and dramatic play. be provided. KiddieCorp can arrange old and new colleagues, attend sessions, The program offers theme activities for meals for children at cost plus 15% or visit the exhibits — and bring your chil- dren! AWM Announces Search for Executive Director

After a short term as Executive Di- and reporting, volunteer efforts, and rector of the Association for Women new initiatives. in Mathematics, Jennifer Quinn has stepped down as of June 30, 2007 to ac- The search for a new executive direc- cept a faculty position at the University tor is now under way. AWM is looking of Washington, Tacoma. “I consider my- for an outstanding individual who is self very fortunate to have served as Ex- passionate about supporting women in ecutive Director of AWM,” says Quinn, mathematics. The part-time position can “It was a rare opportunity to work with be combined with an existing academic many creative, dedicated, and talented appointment via course reductions. women mathematicians.” The AWM office is in the DC area, Over the last few years, AWM has seen but the geographic base of the Execu- many changes — from hiring an asso- tive Director can be anywhere in North ciation management company to hiring America. Nominations, inquiries, and a new Executive Director to restructur- leads may be directed to AWM Presi- ing the Executive Committee with task- dent Cathy Kessel at cbkessel@earthlink. oriented portfolios. During her time as Outgoing AWM Executive Director net. For more information on the posi- Executive Director, Quinn successfully Jenny Quinn. tion and application details see http:// led membership drives, grant writing www.awm-math.org/EDsearch.

23 FOCUS August/September 2007

Building a Successful Actuarial Science Program: Five Key Components

By Mark M. Maxwell An actuary is a business professional programs, 32 have graduate education averaging near 40%. Subsequent exami- who analyzes the financial consequenc- and/or research components. nations have similar pass rates. es of risk. Actuaries use mathematics, statistics and financial theory to study Would developing an actuarial program Many mathematics departments offer a uncertain future events, especially those be beneficial for your students, your de- calculus-based probability course that of concern to insurance and pension partment, your college, and yourself? covers the material on the probability programs. Advancement in the actuarial We believe so. Your students will be exam. Faculty may simply advise stu- profession is predicated upon passing able to apply their mathematics aptitude dents to prepare for the exam, organize a lengthy and arduous series of math- and passion in their professions. Your student study groups, or even conduct ematics-based examinations. Therefore, department and college will benefit from problem-solving study sessions. many actuarial programs are housed a new source of academically talented within mathematics departments. mathematics majors. You will benefit Introductory actuarial science programs from the satisfaction of mentoring mo- have courses that help prepare students Actuaries are valued for their capac- tivated young women and men whose for the 2.5 hour SOA/CAS Exam FM: ity to solve industry problems and de- achievements will make you proud. Financial Mathematics. Geometric se- velop financial forecasting models. As ries are seen in action when present examples, casualty actuaries determine Faculty face inevitable tradeoffs in time values of assets/liabilities are computed auto insurance premiums based on cli- between teaching, service, and research. by discounting cash flows at appropriate ent characteristics like age, gender, However, the investment in actuarial interest rates. driving history, vehicle type, deductible, education can range along a continuum and location. Consulting actuaries de- beginning with minimal advising and Advanced actuarial science courses re- termine pension contributions based on guidance through building an advanced quire highly specialized topics in sur- employee characteristics, work environ- actuarial program. This article will dis- vival and frequency models, life con- ment, and promised benefits within the cuss five important factors in actuarial tingencies, credibility, simulation, and framework of government regulations education that can help you determine construction of parametric models. The and state mandates. Life and health ac- your place along the continuum. advanced examinations and fellowship tuaries perform similar functions when modules are tailored to specific lines of pricing term insurance policies or de- 1. Students should strive to pass as work (finance, investments, individual signing medical plans. many professional examinations as life insurance and annuities, as well as possible group life and health insurance). The There are approximately 21,000 actuar- best employers are generous with study ies credentialed by one of the two major A credentialed actuary has earned some time and resources to support employ- professional societies: the Society of professional designation (EA, ASA, ees as they progress toward an actuarial Actuaries (SOA) and the Casualty Ac- FSA, ACAS, or FCAS). The creden- credential. One can find detailed syllabi tuarial Society (CAS). By comparison, tialing process requires passing a series on the Society web sites, http://www.ca- there are 50 times as many lawyers and of rigorous and comprehensive exami- sact.org and http://www.soa.org. 100 times as many accountants. In its nations while in college and generally last five issues, The Jobs Rated Alma- continuing through the early years of There are benefits to investing long nac consistently ranked actuary as one full-time employment. Exams pose a hours in preparation for an exam that of the top two professions, based upon “trial by ordeal” that clearly identifies you might pass. Exams serve to level the work environment, income, outlook, candidates with the right combination playing field for all students regardless physical demands, security, and stress. of ability and determination. of school or pedigree. Completed exams Actuary was ranked #1 in 1988, #2 (to help employers discriminate between software engineer) in 1992, #1 in 1995, For candidates preparing for an actuarial students more significantly than does # 2 (to webmaster) in 1999, and #2 (to exam, the practiced credo is to study 100 grade point average, work experience, biologist) in 2002. hours for each hour of the exam. This or other traditional résumé items. Pass- translates to 300 hours for the jointly ad- ing subsequent exams will translate to Of the 2593 four-year colleges in the ministered SOA/CAS Exam P/1: Prob- greater employability and increased sal- United States, only 149 are listed by the ability. Preparation time is necessary ary. After graduation, employers contin- SOA as having some kind of actuarial but not sufficient to guarantee success ue to tie compensation rewards and pro- program. There are 78 programs classi- on these exams, with historic pass rates vide study time to progression through fied as introductory. Of the 71 advanced on this calculus-based probability exam the credentialing process. Veteran can-

24 August/September 2007 FOCUS didates long for the good-old college gram requires motivated students. For- 5. Students and alumni — you are days with a dearth of responsibility and tunately, those same students are attract- what you produce a glut of available hours to study. ed to the field. Ultimately an actuarial science program 2. Students should obtain internships Since many high school and college will be defined by the accomplishments students are unaware of this obscure of its students. It is the student who Summer internships should be thought profession, some degree of active en- dedicates months studying hundreds of as well-paid three month job inter- couragement is essential for any level of hours in preparation for the exami- views. Employers evaluate the intern’s of program. Recruiting future actuaries nations. It is the student who develops work ethic, versatility, ability to work may be quite different than recruiting communication skills and represents within their corporate environment, pro- typical college students and is similar to themselves and the program during in- ficiency in writing and presentations, recruiting college athletes. There is of- ternships. It is the student who becomes and capacity to meet deadlines and solve ten a unique recruiting cycle and target tomorrow’s actuary. It is the student who problems. Employers use their intern- audience. Qualified high school students combines business acumen with techni- ship programs to identify talent, often boast attractive academic credentials, cal and communication skills to pursue creating full-time positions for their top are actively recruited by other programs new opportunities. And it is the alumni performing interns. and universities, and receive significant who become the strongest advocates scholarship aid. Ideally, high school for your actuarial program. Those who Gaining a summer internship is a com- sophomores and juniors are contacted. maximize their ability with their work- petitive process with offers frequently Experience shows that a program can ethic and dedication will become the being made in January. Employers develop by word-of-mouth and a few most accomplished students and future might require one actuarial exam passed early success stories of students with ambassadors for your program. and have other filters like class standing, exams passed, internships, and/or re- GPA, or willingness to relocate. Major warding jobs. Risk is Opportunity employers, as well as small boutique ac- tuarial firms, hire skilled students early 4. Faculty should be passionate about Actuarial programs are scalable in terms in college and before passing an exam. the profession of students, faculty, and courses offered. School year internships or cooperative The seed of an actuarial science pro- educational agreements are available at A single dedicated and energetic faculty gram may be a mathematics or finance many universities in proximity to con- member can have a major impact on the professor who counsels a few students sulting or insurance firms. success of students and the growth of an to sit for the calculus-based probability actuarial program. Involved faculty can examination. Growth can include a ded- The best way for a college student to develop relationships with employers, icated class in interest theory and some learn about the various categories of maintain contact with graduates, adjust formal advising. actuarial work is to experience them curriculum, cooperate with other depart- firsthand. A variety of internship expe- ments, recruit students, and stay enlight- The word successful appears in the title riences provides valuable comparisons ened about the profession. An ambitious of this article. What that word means for for students. Internships also provide professor at a smaller school might your university is entirely up to you. In relevant work experience. Students work with enrollment to decide the tar- addition to the five key components al- witness the specific corporate environ- get audience, create direct mail pieces, ready discussed (exams, internships, re- ment, are exposed to the type of work of meet with prospects on campus visits, cruitment, faculty, and students), a full- a company, and network with potential train the revolving door of enrollment blown actuarial program will involve a co-workers. Compensation packages managers, and host various enrollment supportive administration, an effective are consistent between employers and programs. enrollment office, a partnership with it is common for students to select their industry, and an energetic student ac- first actuarial company based upon the Since passing actuarial exams is crucial tuarial club. Initially, relatively modest people they have worked with, not on to a student’s success, faculty must be investments of faculty time can serve to the highest initial salary. On a student willing to provide assistance beyond produce quite rewarding results. résumé, internship experiences are sec- the classroom to those students who ond in importance only to passed exami- are motivated and determined to pass. Mark Maxwell is an Associate Professor nations. Program credibility can be grown with and Program Director of Actuarial Sci- faculty earning an actuarial credential or ence at Robert Morris University. The 3. Programs need to recruit students becoming active in the educational and/ author welcomes all feedback to max- aggressively or research aspects of the profession. By [email protected]. far, the most important and rewarding Due to the nature of the professional tasks for faculty is teaching gifted stu- exam system, a vibrant actuarial pro- dents in and outside of the classroom.

25 FOCUS August/September 2007 Café Scientifique Mathematics in the Microbrewery: Fermat Meets Fermentation?

By Gene Abrams A mathematician walks into a bar. (Do you feel a joke coming on?) Almost 200 people are there, waiting to hear what he’s got to say about current hot topics in mathematics research. (Ready for the punchline?)

Hey, no joke!

It’s clear that over the past decade there has been a significant increase in the profile of mathematics and mathemati- cians in the general media (witness e.g. Good Will Hunting, A Beautiful Mind, Proof, NUMB3RS, etc.). So it probably should not have come as a surprise to me that the general public has developed an interest in what we mathematicians do for a living. In what ranks as one of the most satisfying and rewarding opportu- J.J. Cohen introduces a speaker at the Denver Café Scientifique. Photo by Lisa nities of my career, I had the privilege Litzenberger; used with permission. to share some of what I do with a group of tavern-goers who were thirsting for more than just the local microbrew. This overview is followed by a ten min- mathematics, just as people do basic ute break (to let the patrons refill their science, as well as application-driven Café Scientifique has its origins in the glasses), which is then followed by an mathematics, which is analogous to old French Café Philosophique, a gener- hour of question and answer from those applied science. (I purposefully avoid- al name for a forum in which the general assembled. ed using the phrases “pure” and “ap- public would gather over wine to discuss plied” mathematics.) For the “Next Big the important philosophical issues of the Not certain that there would be any ques- Thing,” I spent ten minutes describing day. General public gatherings to discuss tions (let alone an hour’s worth) from some of the more famous mathematics the important scientific issues of the day the public about mathematics in general, questions (e.g. Fermat’s Last Theorem have recent genesis in the late 1990s in or about what I do in particular, it was and the Four Color Problem), as well as Leeds, England. The oldest Café Scien- with some trepidation that I accepted the Clay Mathematics Institute Million tifique on this side of the Atlantic started Dr. Cohen’s invitation to speak about Dollar Prizes. in Denver in 2003, organized by Dr. J.J. mathematics research in the March 2006 Cohen (a professor of immunology at Denver Café Scientifique. The Denver And just “Why Should You Care?” Of the University of Colorado Health Sci- Cafés are held at the Wynkoop Micro- course we all have our own personal ences Center). Since then an impres- brewery in downtown Denver. Just to answers to that question. What I shared sive number of such monthly gatherings give some context: the February 2006 with this general audience touched first have sprung up throughout the world, Café topic was microbes in the water on the artistic/aesthetic side, then on the including nearly forty active Cafés in supply, while the April ‘06 version dealt “because it’s there/perseverance” side, the United States alone. with a satellite mission to Pluto. and, finally, the “basic science becomes applied science becomes part of your The format of the Cafés is as follows. A I decided to break my 30 minute Math- daily life” side. (Here I talked about scientist chats for 20 to 30 minutes about ematics Research chat into three piec- Fermat’s Little Theorem, then Euler’s some current research work in her/his es: What is it,? What’s the Next Big Generalization, then RSA encryption.) field. No overheads, no Powerpoints, no Thing,? and Why Should You Care? video clips, just talk. (Presenters are al- For the “What is it?” chunk, I described I truly had no idea what to expect when lowed to distribute a one page sheet of how mathematics is not unlike other the patrons returned from the ten minute pertinent information if they so choose.) traditional sciences: people do basic glass-refilling break for the question and

26 August/September 2007 FOCUS answer portion of the evening. What I in Colorado Springs, and at the Redfish got was more than an hour of interest- Brewery in Boulder). While each of ing, well-posed, thoughtful questions those attracted somewhat fewer partici- from all across the mathematical spec- pants, the questions asked were of simi- trum. The first question was from an lar depth and interest. elderly woman who wanted to know how I got interested in mathematics in If there is a Café Scientifique (some- the first place. [I liked science, but hated times also called Science on Tap) in the labs.] A middle aged gentleman then your community, I would strongly urge asked whether Gödel’s incompleteness you to contact the local organizer to see result affected how I approach my re- whether you might arrange to do a pre- search. [Not really for me personally, sentation on mathematics research. See but, for example, I have colleagues are http://www.cafescientifique.org/world- working in areas requiring extensions of links.htm for a list of Café Scientifiques. ZFC.] The Colorado Café homepage is http:// CafeSciColorado.org. For those of you I was nervous that this relatively high- with New York Times access, see http:// brow question about mathematical logic www.nytimes.com/2006/02/21/science/ might stifle additional questions. Just 21cafe.html for an archived news story the opposite! This question was fol- about Café Scientifique. (Thanks to the lowed by a constant stream of inquiries author of that story for the idea which about such topics as: Photo of Gene Abrams used on the spawned the opening few sentences of Café Scientifique web site to promote this article.) • what I personally do research-wise [an his talk. area called Leavitt path algebras which The sheer pleasure you’ll derive from combines graph theory with algebraic dance! (Under Colorado law, minors are the experience will be well worth your structures] allowed to be in a tavern as long as there effort! • whether mathematicians use comput- is food served in the establishment as Gene Abrams is professor of mathemat- ers in their research [not me person- well.) These high school aged students ics at the University of Colorado at ally, but computers have played a role really served as a nice addition to the Colorado Springs. He has been a fac- in many branches of mathematics; I re- discussion. ulty member at UCCS since 1983. He ferred back to the Four Color Problem] And so it went for nearly 90 minutes. is the author or coauthor of over thirty • what role math researchers can play Finally Dr. Cohen had to politely end research articles in mathematics. In in K–12 math education [training of the session. A few people came up to me 1996 he earned lifelong designation as teachers, working directly with K–12 afterwards to ask more questions, and to a University of Colorado system-wide students, and discussion of appropriate share some of their personal experiences President’s Teaching Scholar. In 2002 curricular topics] with mathematics in school (some good, he received the annual Burton W. Jones Outstanding Teaching Award from the • what Fibonacci numbers are, and some not so good). A beautiful end to the evening came when the previously Rocky Mountain Section of the Math- where they come up in real life [spirals ematical Association of America. He in nature] mentioned elderly woman introduced herself to me, then told me that my pas- has been married since 1983 to his wife • whether mathematics is discovered or sion for mathematics left her wanting to Mickey, who sometimes concedes that invented [I think the former, but at least learn more about both mathematics and he is that much fun at home… They have a few of my coauthors argue compel- mathematicians. She then turned to my two children, Ben and Ellen. lingly for the latter] wife and asked “…is he that much fun • what the status of the Poincaré con- at home!?” Have You Moved? jecture is [a discussion of Perelman, the The MAA makes it easy to change As my wife and I drove home that night Fields Medal, and more about the Clay your address. Please inform the I had a sense of overwhelming reassur- Mathematics Institute]. MAA Service Center about your ance that the general public is truly in- change of address by using the elec- By the way, the Poincaré question was terested in what we mathematicians do, and how we go about doing it. Since the tronic combined membership list at asked by a young man who identi- MAA Online http://www.maa.org) fied himself as a high school student. I Denver presentation I have had the op- portunity to do two more Cafés Scienti- or call (800) 331-1622, fax (301) would guess there were at least a few 206-9789, email: maaservice@maa. dozen kids from this age group in atten- fiques (at the Phantom Canyon Brewery org, or mail to the MAA, PO Box 90973, Washington, DC 20090.

27 FOCUS August/September 2007

To and From the Editor

Letters to the Editor about what research on teaching and that information online, freeing up some learning mathematics has discovered. pages for editorial content. So expect to Scholarship of Teaching FOCUS regularly includes brief news see a different October issue! and Learning items and reports in this area, and will continue to do so. Of course, we are a About half of the next issue will con- We couldn’t agree more with James T. news magazine, so our reports will be tain information about the Joint Math- Fey (FOCUS, May/June 2007, “Math- journalistic rather than technical, prac- ematics Meetings, to be held in January ematician Makes Pitch” on page 5) that tical rather than theoretical. in San Diego, CA. The other half will the mathematics community should lend include some news from MathFest, in- its support to the Scholarship of Teach- Mistaken Identity cluding a photo spread, and perhaps a ing and Learning (SoTL) in mathemat- Teaching Time Saver and a few more ics and especially consider such work as I was somewhat puzzled concerning an articles. We’re still trying to figure out appropriate mathematical scholarship. item in the May/June issue of FOCUS. exactly which items need to be in print Toward that end, we note that the MAA In the account of Joe Gallian’s interview and which should stay online. Feedback has offered a minicourse on SoTL at of Doron Zielberger, particular attention from our readers will be very important, the last two national meetings and will is given to something called “Wilf-Ziel- so do let us know whether it worked. again include the Beginner’s Guide to berger algorithmic proof theory.” One the Scholarship of Teaching and Learn- of the things it supposedly proves is the About this Issue… ing in Mathematics among the 2008 identity minicourse offerings. In addition, the We are delighted that the Archive of k 3 MAA sponsored a contributed paper n  2n  ()3n ! American Mathematics Spotlight series session on SoTL in Mathematics at the –1 = is back! Carol Mead, the new archivist, ∑()  n+ k  n!3 2007 Joint Meetings and will co-spon- k=0 promises to continue to send us fascinat- sor with the AMS a Special Session on ing material from the Archives. Teaching Scholarship of Teaching and Learning Is there a misprint involved here (as I Time Savers is another series that is still in Mathematics at the 2008 Joint Meet- suspect there must be)? going strong. I hope our readers enjoy ings. these! Robert Vallin, the new MAA As- Dale Geer sociate Director for Student Programs, Mathematicians and mathematics edu- Oshkosh, WI has provided the first article in a new se- cators have been doing this work as evi- ries, which we call FOCUS on Students. denced by the existence of the SIGMAA Congratulations on your sharp eyes: We hope that both students and their on RUME (Research on Undergraduate there certainly is a mistake! In fact, two teachers and advisors will profit from Mathematics Education). In 1999, Tom misprints, one easy to spot, the other these articles. Banchoff, then President of the MAA, quite tricky. The easy one is to note was one of the first mathematicians to that the fraction in parentheses is actu- About the Future… be selected as a Carnegie Foundation ally meant to be a binomial coefficient. CASTL scholar to investigate questions The hard one to spot is that the range We are continuing to look for articles about teaching and learning (and to date of summation is incorrect. The correct in the What I Learned series, and we more than ten mathematicians have been identity is still hope some more people will stick selected). their necks out and tell us What’s the k 3 n  2n  ()3n ! Best Textbook for various undergradu- –1 = While the steps taken by the MAA ∑ ()   3 ate courses. We also remind readers that k=– n  n+ k n! mentioned above have served to raise we are always looking for interesting the profile of this work, more could be photos, “Found Math” items, and other done. An easy step could be to designate Notes From the Editor filler material. Finally, we hope you will a regular space in one or more of the consider sending us short mathemati- cal articles too: if there’s a cool bit of MAA journals to publish this work. About next Issue… mathematics you can explain in just a few paragraphs, we might be able to use Curtis Bennett Longtime readers of FOCUS know that it. The general guidelines on writing for Jacqueline Dewar for a very long time the April and Oc- FOCUS are online at http://www.maa. Loyola Marymount University tober issues have been dedicated exclu- org/pubs/writingforfocus.html (alterna- sively to information about upcoming tively, click on the “Publications” tab As someone who is both a mathemati- meetings. With the advent and ubiquity and scroll down). cian and a mathematics educator, I am of the World Wide Web, however, it certainly interested in learning more seems possible to move at least a part of

28 August/September 2007 FOCUS

Visiting the “Dark Side” Faculty Fellow By Nora Franzova Programs to Help High School Yes, I have visited the dark side and sional language during all the plenary maybe it is not so dark after all. A col- sessions. Talks by Dennis Pearl and Da- Students league of mine convinced me to attend vid Tall led me to the point of wishing the SIGMAA RUME (Research in Un- to know more. Then Rafael Núñez ad- By Rohitha Goonatilake dergraduate Mathematics) meeting in dressed this issue by analyzing language San Diego on February 22–25, 2007. To and gestures in teaching. I guess I finally The improvement of mathematics be completely honest, San Diego was got an OK from someone to wave my courses in high schools has received the main reason for me attending. I am arms around while teaching. much-needed attention by educational not involved in math education research authorities recently. From algebra to and thus attending a specialized confer- I visited other talks, many by gradu- calculus, students and teachers need any ence seemed a bit far fetched. ate students. I learned to take different possible help that they can get. points of view at my own teaching prac- I consider myself a math purist — I like tices, and also learned that, yes, we all Texas A&M International University, in math for its tricks, puzzles, deep and have to face the same crux when teach- Laredo, Texas, has created a program mysterious connections. But I do spend ing limits, and proofs, and combinator- that has been effective in offering help. most of my working time “selling” this ics, and shifting of graphs, and when our It is called the Faculty Fellows Program. mathematical beauty in undergraduate students are petrified by the “algebra Under this program, members of the uni- courses. Here I was at a meeting where minefield of dysfunctional met-befores” versity faculty interact with local high this selling of mathematics was made (as David Tall put it). The good news is school teachers and their students, form- into an art of its own. that there are great resources available ing a partnership to develop Advanced for those who want to try some other Placement (AP) curricula, encourage What do you do at a conference, where way. students to pursue AP courses, and en- you do not know the professional lan- sure greater success on AP exams. The guage and the etiquette? Of course, you So go ahead, visit the dark side some- faculty fellows visit their assigned high visit the plenary sessions. And those times. It just might shine some light on school as many as two to three times per were wonderful. Already in his first your problems. week and do actual teaching. The high talk, Guershon Harel completely read school students not only benefit from my mind, describing the struggles of Nora Franzova teaches at Langara Col- their teaching, but also get a taste of col- teaching linear algebra. Of course, I was lege in Vancouver, BC. lege teaching. struggling with terminology and profes- Area high schools choose to participate in the program. The participation of uni- Found Math versity faculty is voluntary. Both have been eager to participate. The quality of AP programs is coming under strict Now, the standard public key is they are. To use a simple exam- scrutiny, while at the same time educa- typically a very large prime num- ple, the number fifty might be the tors are pushing to strengthen the aca- demic level of high schools and their ber hundreds of digits long that public key and ten and five would regular offerings. The faculty fellows would take a hundred million PCs, be the private keys. If you know program helped schools offer AP pro- working in parallel several thou- the numbers ten and five you can grams (which parents look for) and in sand years, to figure out the two read the transmission. general to improve their offerings. factors. However, while everyone University faculty learn a lot from such knows the public key number, or (From Simple Genius, by David experiences. More importantly, they can at least your computer does, the Baldacci, described on the jacket make a real difference, both for the stu- only way to read what’s being as presenting “…a stunning world dents and for the schools. sent is by unlocking the public key filled with elite mathematicians, Rohitha Goonatilake is associate pro- using the two private keys. Those physicists, war heroes, spies, and fessor of mathematics at Texas A&M keys are the two prime factors deadly field agents.” Thanks to International University in Laredo, TX. He can be reached by email at harag@ of the public key and only your David Fowler, University of Ne- tamiu.edu. computer software knows what braska–Lincoln.)

29 FOCUS August/September 2007

Teaching Time Savers: Encouraging Contact Early in the Semester

By Chad Westphal Each semester I tend to have a total of during the first week of classes. It can ate names and faces. But the best part 50 to 70 new students, most of whom be during office hours or any time my of it is actually sitting down with happy I’ve never met before. The beginning door is open, as long as they give it to enthusiastic young people who will be of the semester is busy and hectic, but me in person. They’re usually very hap- working hard to do well in my class. it’s important to start out on a positive py to do this — who wouldn’t jump at This is the part of teaching I love. note. I want to quickly learn all of my the opportunity to start the course with students’ names, but at first they all look over 100 percent? For each class, I copy the forms on the same in class. I also want to encour- colored paper, making it easy to dif- age them to ask questions and take ad- When they come in, I glance over the ferentiate between students in different vantage of my office hours, but some questionnaire and ask a few questions: classes. I ask students I already know students can’t muster the nerve to make how do you like your classes, how long to tell me something about them that I a first contact outside class, and - espe have you played the guitar, are you re- don’t already know. For larger classes, cially to admit they don’t understand ally going to work 30 hours per week one could take a quick digital picture of something. If a student falls behind or this semester? These conversations usu- each student during the visit for an ad- has a very weak background, it may take ally last less than five minutes, but they ditional aid. Of course, you can think of me weeks to catch on to this. accomplish several things. ways to make this work best for you.

Even in a small class, it can take half I’m able to put a name with a face very I like to try to get to know my students at of the semester to make sure I have all early in the semester. A short personal some point anyway. This scheme makes the names and faces matched up, unless chat shows that I’m interested in them as this intentional, and getting them one- I really work at it. It’s embarrassing to more than a number, and establishes me on-one early in the semester tends to have to ask a student’s name after the as a nice guy (for awhile at least). The pay off over time. second exam. I’ve found a nice way to weaker students are more likely to seek deal with these issues at the beginning out friendly help before they get behind. Time Spent: 3-5 minutes of non-class of the semester. Though it doesn’t seem And it assures me that they know where time per student at the beginning of the like a real time saver at first, it tends to my office is, allowing me to easily ig- semester. pay off in the long run. nore excuses along those lines later in the semester. Time Saved: It cuts the time to hand On the first day of class I hand out a ques- homework back in half (versus not tionnaire with the standard questions: I find that in this way I can learn all of my knowing names), perhaps 5 minutes per what is your major, what other classes students’ names in the first two weeks. class; perhaps hours of tutoring students are you taking, what are your hobbies, Knowing names early in the semester, behind; and many awkward moments etc. But instead of collecting it in class, I’m able to hand homework back more throughout the semester. I offer a few points of extra credit if they efficiently and to avoid some of those return it to me in my office sometime awkward moments where I can’t associ- Chad Westphal teaches at Wabash Col- lege in Crawfordsville, IN.

FOCUS Deadlines Teaching Time Savers are articles November December January designed to share easy-to-implement Editorial Copy September 16 October 16 November 16 activities for streamlining the day-to- Display Ads September 21 October 26 November 22 day tasks of faculty members every- Employment Ads September 7 October 12 November 10 where. If you would like to share your favorite time savers with the readers of FOCUS, then send a separate email description of each activity to Michael Orrison at [email protected]. Make sure to include a comment on “time spent” and “time saved” for each activity, and to include pictures and/or figures if at all possible.

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31 FOCUS August/September 2007

The Mathematical Association of America ® is celebrating the 300th anniversary of Euler's Birth

The Early Mathematics of Leonhard Euler • C. Edward Sandifer The book gives a portrait of the world's most exciting mathematics between 1725 and 1741, rich in technical detail, woven with connections within Euler's work and with the work of other mathematicians in other times and places. Spectrum • EUL-01 • 416 pp., Hardbound, 2007 • ISBN: 978-0-88385-559-1 • List: $49.95 • MAA Member: $39.95 The Genius of Euler • Reflections on His Life and Work William Dunham, Editor The book is a testimonial to a mathematician of unsurpassed insight, industry, and ingenuity--the one who has been rightly called "the master of us all." The collected articles, aimed at a mathematically literate audience, address aspects of Euler's life and work, from the biographical to the historical to the mathematical. Spectrum • EUL-02 • 324 pp., Hardbound, 2007 • ISBN: 978-0-88385-558-4 • List: $47.95 • MAA Member: $38.50

How Euler Did It • C. Edward Sandifer How Euler Did It is a collection of 40 monthly columns that appeared on MAA Online between November 2003 and February 2007 about the mathematical and scientific work of the great 18th-century Swiss mathematician Leonhard Euler. Spectrum • EUL-03 • 304 pp., Hardbound, 2007 • ISBN: 978-0-88385-563-8 List: $51.95 • MAA Member: $41.95 Euler and Modern Science N.N. Bogolyubov, G.K. Mikhailov, and A.P. Yushkevich, Editors We speak of the “Age of Euler.” A justification for this term is provided by the list of scientific terms connected with Euler's name and his many contributions to pure mathematics, well-known in the mathematics communi- ty and, in part, covered in this volume. This collection contains an extensive treatment of Euler's contributions outside pure mathematics. Spectrum • EUL-04 • 425 pp., Hardbound, 2007 • ISBN: 978-0-88385-564-5 •List: $59.95 • MAA Member: $47.95 Euler at 300 • An Appreciation Robert E. Bradley, Lawrence A. D'Antonio, and C. Edward Sandifer, Editor

During the years leading up to Leonhard Euler's tercentenary, at more than a dozen academic meetings across the USA and Canada, mathematicians and historians of mathematics honored Euler in papers detailing his life and work. This book collects more than 20 papers based on some of the most memorable of these contribu- tions. Spectrum • EUL-05 • 325 pp., Hardbound, 2007 • ISBN: 978-0-88385-565-2 •List: $51.95 • MAA Member: $41.95 Order all 5 books and save 10% Catalog Code: EULSET • List: $235.75 • MAA Member: $189.25 To order visit us

online at: The Mathematical Association of America Periodicals Postage paid at To Order: 1529 Eighteenth St., NW Washington, DC and www.maa.orgWashington, DC 20036 additional mailing offices orCall: call us at: 1.800.331.1622 1.800.331.1622or Online at www.maa.org

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